A285062 Numerators of the exponential expansion of (4/(log(1+x)))*(1-1/(1+x)^(1/4)).

1, -1, 7, -81, 3853, -25721, 1862773, -52571875, 2828694491, -20554196553, 2489317910533, -36843139557745, 187344440646279463, -200535626786994961, 15853768141768274581, -319644021424695652161, 927777140067161706072467, -1412565248386878259675625, 2151379749437782936765977859

Offset

0,3

Comments

This gives the numerators of the z-sequence for the Sheffer triangle (exp(x), exp(4*x) - 1) shown in A285061. For the notion and use of a- and z- sequences for Sheffer triangles see the W. Lang link under A006232. The a-sequence of this Sheffer triangle is given by 4*A006232/A006233.

For the nontrivial recurrence for the sequence {1^n} of column m=0 of A285061 by the z-sequence see the example n=4 below.

Links

Table of n, a(n) for n=0..18.

Formula

The e.g.f. of the rationals r(n) = a(n)/A285063(n) is (4/(log(1+x)))*(1 - 1/(1+x)^(1/4)).

Example

The rationals r(n) = a(n)/A285063(n),  n >= 0,  start: 1, -1/8, 7/48, -81/256, 3853/3840, -25721/6144, 1862773/86016, -52571875/393216, 2828694491/2949120, -20554196553/2621440, ...
The z-Recurrence for A285061(4, 0) = 1 is  1 = 4*(1*1 + 124*(-1/8) + 240*(7/48) + 64*(-81/256)).

Crossrefs

Cf. A006232, A006232/A006233, A285061.

Sequence in context: A058575 A355220 A375475 * A253265 A338684 A304870

Adjacent sequences: A285059 A285060 A285061 * A285063 A285064 A285065

Keyword

sign,frac,easy

Author

Wolfdieter Lang, Apr 13 2017

Status

approved